1. Field of the Invention
The present invention relates to a thresholding method for segmenting gray scale images and a method for determining a background concentration distribution in such an image processing as pattern matching and pattern checking, and also to an image displacement detection method in an image processing of image alignment for patterns such as an LSI pattern, letter pattern, and print pattern.
2. Description of the Background Art
Conventionally, as a thresholding method based on the concentration distribution which is to be utilized in the pattern matching and pattern checking by a computer, a p-tile method and a mode method are known.
The p-tile method is a method in which a threshold is selected to be such a concentration value by which a cumulative concentration distribution of the input image calculated sequentially from the lowest concentration value reaches to a prescribed value p.
However, this p-tile method has a limitation in that the prescribed value p must be known in advance so that it cannot be utilized as a general thresholding method. Thus, in order for this p-tile method to be applicable, it is necessary that there exists a standard pattern to be compared with, a positional relationship of the input image and the standard pattern is already known, and the input pattern does not include any defect or excessive pattern.
The mode method is a method in which a threshold is determined to be a concentration value corresponding to a valley of a presumed bimodal concentration distribution for the input image.
This mode method is capable of determining the threshold in a case the pattern portion and the background portion have the similar shape of the concentration distribution and occupy approximately the same area, but is unable to obtain the appropriate threshold otherwise because the valley of the bimodal concentration distribution shifts its position toward the portion occupying the smaller area as the ratio of the occupied areas deviates from a value of 1:1.
In addition, as a general thresholding method, there is a discriminant analysis method in which a threshold is determined to be a concentration value at which a separability of the concentration distribution in a case of dividing the concentration distribution into two becomes maximum.
However, this discriminant analysis method has the problem similar to the mode method described above in that it is unable to obtain the appropriate threshold in a case other than that in which the pattern portion and the background portion have the similar shape of the concentration distribution and occupy the approximately the same area, because the separability deteriorates significantly when the area occupied by the pattern portion is small.
Now, the shading correction for the image showing the LSI pattern utilizes the knowledge of the background concentration distribution, and this background concentration distribution has conventionally been determined by using a method in which the background concentration distribution is determined by inputting an image of the background only, so that this method depends on a unique characteristic of the image input device.
On the other hand, there is also known a method of determining the background concentration distribution which depends on the pattern distribution in the input image. In this method, the background concentration distribution is determined by distinguishing the pattern portion and the background portion in the input image and obtaining the concentration distribution of the background portion only, so that it is necessary for the background portion to be distinguishable from the pattern portion.
However, in a case of a scanning electron microscope (SEM) image of an LSI wafer, there is a fluctuation in the background concentration distribution in correspondence with the pattern distribution because of the charging up by the electrons, so that there is a need for performing the shading correction in the image processing of the pattern portion recognition. Yet, the shading correction requires the knowledge of the background concentration distribution which cannot be obtained without the knowledge of the pattern portion recognition conventionally.
Now, as a conventional image displacement detection method for detecting a displacement of an image for patterns such as an LSI pattern, a letter pattern, and a print pattern, a local correlation method has been known.
In this local correlation method, a local image obtained from the standard image is utilized as a template, and the correlation value is calculated as this template is moved over the image, such that the displacement is detected by taking a state of matching for which the correlation value becomes maximum.
There are further propositions to reduce an amount of calculation involved by changing the definition of the correlation function. In this respect, the SSDA method can also be regarded as one variation or modification of the correlation method.
As a method of significantly reducing an amount of calculation in the correlation method, there is a proposition for utilizing cumulative projection patterns on the input image along two directions. Such a proposition can be found in Japanese Patent Application 2-18899 in which this method is used as a preliminary adjustment to be used in conjunction with some other fine adjustment.
However, this method of cumulative projection pattern comparison has the problem of a possibility for a period mismatching error to occur in dealing with the repetitious pattern image.
Such a period mismatching error occurs for example for a case of pattern matching a designed reference pattern (standard pattern) 1 shown in FIG. 1(A) and an observed LSI pattern (object pattern) 2 shown in FIG. 1(B), where it is assumed that the image displacement correction for the observed pattern 2 is already made. In the cumulative projection pattern comparison method, the image displacement correction is determined according to an X-direction cumulative projection pattern 3 and a Y-direction cumulative projection pattern 4 for the designed reference pattern 1 as well as an X-direction cumulative projection pattern 5 and a Y-direction cumulative projection pattern 6 for the observed pattern 2. In this example, the X-direction cumulative projection patterns 3 and 5 completely coincide with each other and the Y-direction cumulative projection patterns 4 and 6 also completely coincide with each other, so that according to the cumulative projection pattern comparison method it is concluded that the observed pattern 2 of FIG. 1(B) is identical to the designed reference pattern 1 of FIG. 1(A), which is apparently false as can be seen in FIGS. 1(A) and 1(B). This false result is obtained because of the period mismatching error which cannot be discerned from the data on the X- and Y-direction cumulative projection patterns alone.
Here, it is possible to detect this occurrence of the period mismatching error by taking the correlation from the superposition of the designed reference pattern 1 and the observed pattern 2, but the inclusion of such an additional operation causes the significant increase of the amount of calculation, and this in turn obliterates the most advantageous feature of the cumulative projection pattern comparison method. Thus, this method has not been applicable for the image of a repetitious pattern.